Just three months ago, WPP acquired a majority stake in AKQA, one of the world's biggest and most well-known digital ad agencies, in a $540m (£332m) deal.

Amsterdam-listed LBi reported earnings before interest, tax, depreciation and amortisation (ebitda) of €19.9m for the first half of 2012, implying that Publicis Groupe has paid a multiple of about 10.5 times profits.

Sorrell paid a multiple of about 12.8 times ebitda for AKQA.

Publicis said the offer for LBi, which has so far been accepted by investors controlling 67% of stock, was a 39.8% premium on its share price before speculation of a sale emerged in June.

"The acquisition of LBi is another step forward in further strengthening our digital operations," said Levy, adding that the deal would mean that more than 35% of Publicis Groupe's total revenues will now come from digital operations.

UBS advised Publics Groupe on the deal, while LBi was advised by Jefferies.

LBi was prompted to put out a statement to the stock market admitting it was in talks with interested parties, of which Publicis was considered by observers to be the most likely buyer, days after Sorrell acquired AKQA in June.

Levy has been on something of a digital buying spree in recent years.

In 2006, Publicis spent $1.3bn on Digitas and in 2010 paid Microsoft $530m for the Razorfish ad agency network.

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